2016
DOI: 10.48550/arxiv.1601.07058
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Trapezoidal numbers, divisor functions, and a partition theorem of Sylvester

Abstract: A partition of a positive integer n is a representation of n as a sum of a finite number of positive integers (called parts). A trapezoidal number is a positive integer that has a partition whose parts are a decreasing sequence of consecutive integers, or, more generally, whose parts form a finite arithmetic progression. This paper reviews the relation between trapezoidal numbers, partitions, and the set of divisors of a positive integer. There is also a complete proof of a theorem of Sylvester that produces a… Show more

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